A service station has three servers, indexed 1, 2, and 3. When a customer arrives, he is assigned to the idle server with the lowest index. If all servers are busy, the customer goes away. The service times at server i are i.i.d. and exponentially distributed with rate i (i = 1, 2, 3), and are independent for different servers. Different i 's represent different speeds of the servers. The customers arrive according to a Poisson process with rate . Model this system as a CTMC and find its rate diagram and generator matrix.